Tamara invested \( \$ 15,000 \) in a money market account with an interest rate of \( 2.25 \% \) compounded semiannually. Five years later, Tamara withdrew the full amount to put toward the down payment on a new house. How much did Tamara withdraw from the account? Tamara withdrew \( \$ \square \) (Round to the nearest cent as needed.)

To calculate how much Tamara withdrew from her money market account after 5 years, we can use the compound interest formula: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] where: - \( A \) is the amount of money accumulated after n years, including interest. - \( P \) is the principal amount (the initial amount of money). - \( r \) is the annual interest rate (decimal). - \( n \) is the number of times that interest is compounded per year. - \( t \) is the time the money is invested for in years. For Tamara's investment: - \( P = 15,000 \) - \( r = 0.0225 \) (2.25% as a decimal) - \( n = 2 \) (since interest is compounded semiannually) - \( t = 5 \) Substituting the values into the formula: \[ A = 15000 \left(1 + \frac{0.0225}{2}\right)^{2 \times 5} \] Calculating the values inside the parentheses: \[ A = 15000 \left(1 + 0.01125\right)^{10} \] \[ A = 15000 \left(1.01125\right)^{10} \] Calculating \( (1.01125)^{10} \): \[ (1.01125)^{10} \approx 1.116646 \] Now, importing that back into the equation for \( A \): \[ A \approx 15000 \times 1.116646 \approx 16749.69 \] Thus, rounding to the nearest cent, Tamara withdrew approximately \( \boxed{16749.69} \).